MA354 Introduction to Building Models: Models Select, Describe and Predict Relationships Between Variables

Functional Relationships Among Variables x,y No Relationship –Or effectively no relationship. –No need (and not useful) to use x in describing y. Proportional Relationship –Or approximately proportional. –x = k*y Inversely proportional relationship –x=k/y More complex relationship –Non-linearity of relationship often critical –Exponential –Sigmoidal –Arbitrary functions

A Relationship Between Two Quantities Points to an interaction –May be direct –May be indirect An appropriate model correctly describes their interaction at a level of complexity needed to address a question of interest Example: oranges and soap bubbles both form spheres, but for different reasons  Some models are actually analogies.

Example: Hooke’s Law An ideal spring. F=-kx x = displacement(variable) k = spring constant(parameter) F = resulting force vector

Other Examples Circumference of a circle is proportional to r Weight is proportional to mass and the gravitational constant Etc.